Was looking at your request for help and was restricted by a lack of dates. Tullamaine seems to be a few miles NE of the town of Callan so if they were Christians, they should have been baptised in a local mission Church or in the main Church in Callan itself. You should be able to calculate rough dates for your own grandmother and with a little luck you could get back one more generation to Philip. Who emigrated? Was it Philip or one of the kids?
The only place Tullamine appears is in the 1901 census. There is no record of people staying there in the 1911 census. But there are no Byrnes in residence in 1901. See this link. http://www.census.nationalarchives.ie/search/results.jsp?searchMoreVisib...
Came accross one Byrne in Griffith's Valuation from the mid 1800's. This record is probably from 1850. His name is given as Bryan Byrne. http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doName...(flood)
I hope this is of some help. Let me know if I can help further.